[EM] Optimal Cardinal Proportional Representation

[Kevin Venzke]

Hi Toby,

> I posted the below on the Voting Theory Forum, but thought it might be of
> interest to some people on this list as well. The link formatting won't work
> here in the same way, but URLs can simply be copied and pasted. It should
> still read OK, and I'd be more likely to make a mess of it by changing
> everything around.

> The problem is that there are essentially two orthogonal goals for a method -
> maximising proportionality and also being properly monotonic (as well and
> passing things like [Independence of Irrelevant Ballots]
> (https://electowiki.org/wiki/Independence_of_Irrelevant_Ballots)) - and there
> was never any guarantee that they could be seamlessly combined.

I do find this interesting and will have to look into all this... I started
working on a PAV calculator but ended up finding the topic to be bigger than I
thought.

I understand the satisfaction function of Thiele's methods (sequential or just
finding the best set of winners). Discovering seq-Phragmén, I liked the concept
of candidates "costing" a fixed amount to be borne by a candidate's supporters,
but as I understand it the specific load borne by a given voter can vary, in
particular with the effect of "charging" a voter more for the election of a given
candidate precisely because that voter hadn't managed to elect anyone yet. That
doesn't strike me as fair, or reflective of anything. Maybe I misunderstand it.

One thought I had is maybe the most helpful thing would be a webpage where users
could play around with selecting sets of winners and see evaluations of those
sets by some metrics. This, as opposed to focusing on the results of specific
methods.

Not sure if you have any thoughts on what an ideal tool would do.

Kevin
votingmethods.net